Some Curvature Tensor Relations on Nearly Cosymplectic Manifolds with Tanaka-Webster Connection

Year 2022, Volume: 5 Issue: 1, 24 - 31, 15.03.2022

Gülhan Ayar

https://doi.org/10.32323/ujma.1067101

Cited By: 2

Abstract

In this article, some curvature properties with respect to Tanaka-Webster connection on nearly cosymplectic manifolds have been studied.

Keywords

nearly cosymplectic manifolds , Tanaka-Webster connection , curvature tensor

References

• [1] G. Ayar, H.R. Cavusoglu, Conharmonic curvature tensor on nearly cosymplectic manifolds with generalized tanaka-webster connection, Sigma J. Eng. Nat. Sci, 39(5), (2021), pp. 9–13.
• [2] G. Ayar, P. Tekin, N. Aktan, Some Curvature Conditions on Nearly Cosymplectic Manifolds, Indian J. Industrial Appl. Math., 10(1), (2019), 51-58.
• [3] G. Ayar, M. Yildirim, Nearly cosymplectic manifolds with nullity conditions, Asian-Eur. J. Math., 12(6), (2019), 2040012 (10 pages). doi: 10.1142/S1793557120400124.
• [4] D.E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Math., 509, (1976), Springer-Verlag, Berlin.
• [5] D.E. Blair, Almost Contact Manifolds with Killing Structure Tensors, I. Pac. J. Math., 39, (1971), 285-292.
• [6] D.E. Blair, S.I. Goldberg, Topology of almost contact manifolds, J. Differential Geom., 1, (1967), 347-354.
• [7] S.K. Chaubey, R.H. Ojha, On the m-projective curvature tensor of a Kenmotsu manifold, Differ. Geom. Dyn. Syst., 12, (2010), 52-60.
• [8] S.K. Chaubey, Some properties of LP-Sasakian manifolds equipped with m-projective curvature tensor, Bull. Math. Anal. Appl., 3(4), (2011), 50-58.
• [9] S.K. Chaubey, On weakly m-projectively symmetric manifolds, Novi Sad J. Math., 42(1), (2012), 67-79.
• [10] B.Y. Chen, Geometry of submanifolds, Pure Appl. Math., 22, (1973), Marcel Dekker, Inc., New York.
• [11] D. Chinea, M. de L´eon, J.C. Marrero, Topology of cosymplectic manifolds, J. Math. Pures Appl., 72(6), (1993), 567-591.
• [12] A. De Nicola, G. Dileo, I. Yudin, On Nearly Sasakian and Nearly Cosymplectic Manifolds, Annali di Mat. , 197(1), (2018), 127-138.
• [13] U.C. De, G. Ghosh, On Generalized Tanaka-Webster Connection In Sasakian Manifolds, Bull. Transilv. Univ. Brasov 2- Ser. III: Math., Inf., Ph., 9(58), (2016), 13-24.
• [14] A. Dundar, N. Aktan, Some Results on Nearly Cosymplectic Manifolds, Univers. J. Math. Appl., 2(4),(2019), 218-223, DOI: 10.32323/ujma.625939.
• [15] H. Endo, On the Cur vature Tensor of Nearly Cosymplectic Manifolds of Constant f-sectional curvature, An. Stiit. Univ. ”Al. I. Cuza” Iasi. Mat. (N.S.), (2005), 439-454.
• [16] D. Friedan, Non linear models in 2+edimensions, Ann. Phys., 163, (1985), 318419.
• [17] A. Gray, Nearly Kahler Manifolds, J. Differential Geom., 4, (1970), 283-309.
• [18] P. Libermann, Sur les automorphismes infinit esimaux des structures symplectiques et de atructures de contact, oll., G’eom. Diff. Globale, (1959), 37-59.
• [19] B.C. Montano, Some remarks on the generalized Tanaka-Webster connection of a contact metric manifold, Rocky Mountain J. Math., 40(3),(2010), 1009-1037.
• [20] I. Unal, M. Altin, N(k)-contact Metric Manifolds with Generalized Tanaka-Webster Connection, Filomat, 35(4), (2021).
• [21] D.G. Prakasha, B.S. Hadimani, On The Conharmonic Curvature Tensor Of Kenmotsu Manifolds With Generalized Tanaka-Webster Connection, Miskolc Math. Notes, 19(1), (2018), 491-503.
• [22] G.P. Pokhariyal, R.S. Mishra, Curvature tensor and their relativistic significance II, Yokohama Math. J., 19, (1971), 97-103.
• [23] R. Sharma, Certain results on K-contact and (k;m)􀀀contact manifolds, J. Geom., 89, (2008), 138-147.
• [24] S. Tanno, The automorphism groups of almost contact Riemannian manifold, Tohoku Math. J., 21, (1969), 21-38.
• [25] M. Yildirim, S. Beyendi, Some notes on nearly cosymplectic manifolds, Honam Math. J., 43(3), (2021), 539–545. https://doi.org/10.5831/HMJ.2021.43.3.539.
• [26] K. Yano, S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Differential Geom., 2, (1968), 161-184.